'I will share with you an anecdote that Lacan confided to me. He admitted to his friend Roman Jakobson his difficulty with the title of his next Seminar. "Whenever this happens to me", replied the eminent linguist, "I always say 'Problems'".

I attribute this difficulty to the major turning point marked by this Seminar. Each of the early Seminars was appended to one of Freud's works, on which he offered an admittedly digressive, extensive commentary. Seminar XI, on The Four Fundamental Concepts, was effectively a final synthesis of this first period. The second begins with our Crucial Problems. From that point on, the Seminars will focus on Lacan's own original and unmediated contribution.

Despite the scattered themes in the present Seminar, consistent with its title, it nevertheless has a centre, according to Lacan, in "the being of the subject". But do pay attention! This subject is the Lacanian subject, $, which is to say, divided and split, and has nothing to do with the unity of the ego. Is it a concept? A writing, more likely, in multiple senses. It does not permit of being locked down in a definition; it is only to be approached by a series of formulas and figures.

One formula stands out: "the signifier represents the subject for another signifier", which is a transformation of the definition of a sign as representing something for someone. Topological figures, the famous Möbius strip first and foremost, illustrate different states of the subject's structure. Crucial Problems. constitutes a re-departure for Lacan's teaching. Many of the developments to come commence here.'

Jacques-Alain Miller